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Proof step 9 from proof addarray-negative (previous step)

okarray(r, ty, addarray(r, ty, i, st)), i < 0 ⊦ r = jvmref

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ okarray(r, ty, st) ↔ okreftype(refval(r), mkarraytype(ty), st) ∧ r ≠ jvmref ∧ r -- _length ∈ st ∧ is_integervalue(st[r -- _length]) ∧ 0 ≤ st[r -- _length] .intval ∧ is_arrayref(r, st[r -- _length] .intval, st) ∧ (∀ j. 0 ≤ j ∧ j < st[r -- _length] .intval → oktype(st[r -- j '], ty, st))
Proof step 6:
⊦ okreftype(refval(r), mkarraytype(ty), addarray(r, ty, i, st))
Proof step 7:
⊦ r -- _length ∈ addarray(r, ty, i, st)
Proof step 8:
⊦ (addarray(r, ty, i, st)[r -- _length]) = intval(i)

Rule argument

[speclemmaarg: , okarray(r, ty, st) ↔ okreftype(refval(r), mkarraytype(ty), st) ∧ r ≠ jvmref ∧ r -- _length ∈ st ∧ is_integervalue(st[r -- _length]) ∧ 0 ≤ st[r -- _length] .intval ∧ is_arrayref(r, st[r -- _length] .intval, st) ∧ (∀ j. 0 ≤ j ∧ j < st[r -- _length] .intval → oktype(st[r -- j '], ty, st)) ,[st, ty, r] → [addarray(r, ty, i, st), ty, r] ,F ,okfuns , ,okarrayNotNull ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ is_integervalue(intval(i))], [CSIMPSEQ : ⊦ intval(i) .intval = i], [CSIMPSEQ : ⊦ i < j → (¬ ¬ j ≤ i ↔ false)])], [EXTRATERMS : (addarray(r, ty, i, st), ty, r)]]